I keep my cleanser in the shower and my other products in the shower room too, the only exception is i might sometimes put the BP in the fridge, it feels a lot nicer, I would at least keep the BP in a cuppord if I where you, but if you can't it doesn't matter that much

I only put the cleanser in the shower when I am showering. I take it out after. However, I think it's okay to leave in. It is possible for steam to enter, but all that would do is water it down and the cleanser is very strong as is. I wouldn't worry about it unless you have several people taking hot showers every day. And if you are worried about it, then just take it out. A clear mind is worth a lot.

I'm unaware of any issue with this as most people do tend to store it in the shower. You definitely do not want to store jojoba oil in there though. Keep the jojoba, moisturizer and bp in a cool dry place such as a cabinet.